Random Response Of Vibro-impact System To Stochastic Excitation

Non-smooth systems are generated since the existence of all kinds of non-smooth factors, andthese systems often occur in technological situations. The nonlinearity, even strong nonlinearity,which is derived because of the presence of the non-smooth factors, induces many interestingphenomena in these systems. Vibro-impact system is an important kind of non-smooth systems as aresearch object, this paper analyses the response and stability of these systems, the robustness of thesystem under the effect of noise is also discussed in paper. The main works are as follows:Firstly, the approximate stationary responses of an SDOF unilateral vibro-impact system wereobtained by using the stochastic averaging method for strongly non-linear system under wide-bandrandom excitation, where the so-called general harmonious function method is applied during such anapproach. The analytical results present in this paper shows that stationary probability densities ofamplitude, total energy, and displacement and velocity of the system agree well with those fromnumerical simulations of the original equation of the system. The influence of some parameters of thesystem on the stationary probability density is also discussed at last in this paper.Secondly, the resonance response and moment stability of vibro-impact system with a one-sidedbarrier to boundary random parametric excitation are investigated, the analysis is based on a specialZhuravlev transformation, which reduces the system to one without impacts, or velocity jumps,thereby permitting the applications of asymptotic averaging over the period for slowly varyingrandom process. The linear stochastic transformation is taken to obtain the eigen-value problemgoverning the pth moment Lyapunov exponent. The analytical expression of the largest Lyapunovexponent is obtained in the case when there are no random disturbance, while the pth momentLyapunov exponent is obtained numerically in the case when the random disturbance exist.Finally, based on the models obtained from practical problems, the responses of the Duffingoscillator with single-sided barrier and a two-degree-of-freedom vibro-impact system to combinedharmonic and random excitation are investigated. Some special phenomena are found in these systems,like grazing bifurcation, period-doubling bifurcation. It is also found that the effect of the presence ofnoise is not completely like smooth system, and in some critical situations, the noise can even changethe property of the system.